Presence Of Modeling Errors Research Articles

Nonlinear system identification using wavelet networks

A novel identification scheme using wavelet networks is presented for nonlinear dynamical systems. Based on fixed wavelet networks, parameter adaptation laws are developed using a Lyapunov synthesis approach. This guarantees the stability of the overall identification scheme and the convergence of both the parameters and the state errors, even in the presence of modelling errors. Using the decomposition and reconstruction techniques of multiresolution decompositions, variable wavelet networks are introduced to achieve a desired estimation accuracy and a suitable sized network, and to adapt to variations of the characteristics and operating points in nonlinear systems. B-spline wavelets are used to form the wavelet networks and the identification scheme is illustrated using a simulated example.

A methodology for on-line setpoint modification for batch reactor control in the presence of modeling error

Batch and semi-batch reactors are usually highly nonlinear and involve complex reaction mechanisms. Often, the lack of rapid direct or indirect measurements of the properties to be controlled makes the process control task very difficult. It is the usual practice to follow the prespecified setpoint profiles for process variables for which measurements are available, e.g., temperature, in order to obtain desired product properties. Model error can be the cause of poor performance when these setpoint profiles based on a model are implemented on the actual plant. This paper formulates a state estimation model based algorithm for on-line modification of setpoint profiles utilizing infrequent and delayed measurement information of the properties to be controlled, with the goal of obtaining the desired values of the properties in the minimum batch time. The algorithm modifies the setpoint profile for the remainder of the batch after every such measurement by making one step in the right direction instead of attempting to find a completely new optimal profile. This results in robustness with respect to model error and allows improvement even with infrequent product property measurements. The implementation of the setpoint profiles is made via real-time observer based nonlinear quadratic dynamic matrix control, which has been studied extensively in the literature. The modest additional on-line computational requirements of the proposed method offer promise for the practical on-line implementation. The effectiveness of the algorithm is demonstrated with simulations for bulk polymerization of styrene.

Robust output feedback stabilization of the angular velocity of a rigid body

The problem of semi-global stabilization of the angular velocity of an under-actuated rigid body in the presence of model errors is addressed and solved using a smooth, time-varying, dynamic, output feedback control law. The proposed scheme improves some of the existing results and provides guidelines for a general stabilization strategy applicable to systems which are not exponentially stabilizable. Simulations results are included.

Comparison of dead time compensation schemes for discrete implementation of the Q-PID algorithm

A PID type algorithm called Q-PID was developed to improve online quality control of continuous processes. It has adjustable parameters to improve the controlled variable response or to decrease the manipulated variable movements, hence decrease the cost of control. Q-PID has PID type terms, a lead/lag term and dead time compensation. All previously published work using this algorithm considered continuous systems. Discrete implementation must be analyzed so that it can be used practically. This paper presents a sound development and simulation of the three possible dead time implementation schemes, Smith predictor, analytical predictor, and generalized analytical predictor that could be used for discrete implementation. It was discovered that either the Smith predictor or analytical predictor techniques could be used in the Q-PID with satisfactory results. The generalized analytical predictor results in drastic cost increases and instability in the presence of modeling error. The Smith predictor is the suggested method as it performs the best in the presence of modeling error and is simple and easy to implement.

Exponential Stabilization of a Wheeled Mobile Robot Via Discontinuous Control

In the present work the problem of exponential stabilization of the kinematic and dynamic model of a simple wheeled mobile robot is addressed and solved using a discontinuous, bounded, time invariant, state feedback control law. The properties of the closed-loop system are studied in detail and its performance in presence of model errors and noisy measurements are evaluated and discussed.

Variable neural networks for adaptive control of nonlinear systems

This paper is concerned with the adaptive control of continuous-time nonlinear dynamical systems using neural networks. A novel neural network architecture, referred to as a variable neural network, is proposed and shown to be useful in approximating the unknown nonlinearities of dynamical systems. In the variable neural networks, the number of basis functions can be either increased or decreased with time, according to specified design strategies, so that the network will not overfit or underfit the data set. Based on the Gaussian radial basis function (GRBF) variable neural network, an adaptive control scheme is presented. The location of the centers and the determination of the widths of the GRBFs in the variable neural network are analyzed to make a compromise between orthogonality and smoothness. The weight-adaptive laws developed using the Lyapunov synthesis approach guarantee the stability of the overall control scheme, even in the presence of modeling error(s). The tracking errors converge to the required accuracy through the adaptive control algorithm derived by combining the variable neural network and Lyapunov synthesis techniques. The operation of an adaptive control scheme using the variable neural network is demonstrated using two simulated examples.

Multi-input multi-output control of a continuous fermenter using nonlinear model based controllers

Internal Model Control (IMC) and Model Predictive Control (MPC), the two most important members of model based controllers, are favourable alternatives for control of nonlinear processes. However, the performance of these controllers deteriorates drastically in the presence of substantial process-model mismatch. Hu and Rangaiah (1998) proposed feedback augmentation for nonlinear IMC (hence named Augmented IMC, AuIMC) for improving control in the presence of modelling errors, and demonstrated its success on a neutralization process. In the present study, IMC, MPC and AuIMC strategies are tested in a more difficult case of multi-input multi-output (MIMO) operation of a highly nonlinear continuous fermenter. A new control configuration is introduced as the conventional configuration is not applicable. Simulation results for different modelling errors show that IMC is better than MPC for fermenter control. The advantage of augmentation as in AuIMC manifests in the significantly improved regulatory control of the fermenter.

DELAYED-X LMS ALGORITHM: AN EFFICIENT ANC ALGORITHM UTILIZING ROBUSTNESS OF CANCELLATION PATH MODEL

In conventional ANC (Active Noise Control), the cancellation path is usually modelled by a FIR filter with many coefficients. In this study, a Delayed-X LMS algorithm is investigated of which the computational load is much less than that of the Filtered-X LMS method for a long duct or narrow band noise cancellation application. This algorithm is based on the hypothesis that the cancellation path model for the Filtered-X LMS method does not have to be accurate and can be represented by a delay in such cases. The steady state weight vector solution in the presence of model error is investigated to show the validity of using an erroneous simplification. The ADE (Adaptive Delay Estimation) method is proposed for effective delay estimation of the cancellation path, which can be used with the Delayed-X LMS algorithm on-line or off-line. Simulation and experimental results demonstrate the effectiveness of the Delayed-X LMS algorithm for the specified applications.

An adaptive optimal control scheme based on hybrid neural modelling

A hybrid neural modelling procedure which enables the implementation of an adaptive control scheme for the optimization of fed-batch fermentations is presented. Simulations for the processes of cell mass production and ethanol fermentation by Sacharomyces cerevisae show that, in the presence of modelling errors, the adaptive control leads to nearly optimal results, while open-loop control leads to bad results. Experimental studies show that, for the process of ethanol fermentation by Zymomonas mobilis, a hybrid neural model can be developed with relatively few experimental data and the use of an approximate mathematical model.

Array processing techniques for multiuser detection

Techniques often used in the area of adaptive array signal processing are applied to the multiuser detection problem. The results of this effort include a robust detector, suitable for use in the presence of modeling errors, and a reduced-rank detector with improved transient behavior relative to full-rank detectors. Algorithm performance is presented in the form of bit-error-rate (BER) curves and least mean square (LMS)-like learning curves.

Fuel-efficient pulse command profiles for flexible spacecraft

A procedure for designing command profiles for flexible spacecraft is presented. The command profiles are designed to maneuver a spacecraft with very little residual vibration, even in the presence of modeling errors. To model the case where a spacecraft is equipped with on-off reaction jets, the command signals are restricted to positive or negative constant-amplitude pulses. The technique results in command profiles that are much more fuel efficient than the time-optimal commands, yet do not incur a significant time penalty. Robustness to modeling errors of both the time-optimal and the fuel-efficient commands are shown to be highly dependent on move distance; however, the fuel-efficient profiles are always as robust as the time-optimal profiles.

Variable Neural Networks for Nonlinear Adaptive Control

This paper is concerned with the adaptive control of continuous-time nonlinear dynamical systems using neural networks, A novel neural network architecture, referred to as a variable neural network, is proposed and shown to be useful in approximating the unknown nonlineanties of dynamical systems. In variable neural networks, the number of basis functions can be either increased or decreased with time according to specified design strategies so that the network will not overfit or underfit the data set. Based on the Gaussian radial basis function variable neural network, an adaptive control scheme is presented. The location of the centres and the determination of t.he widths of the Gaussian radial basis functions in the variable neural network are analyslzed to make a compromise between orthogonality and smoothness. The weight adaptive laws developed using the Lyapunov synthesis approach guarantee the stability of the overall control scheme, even in the presence of modelling errors. The tracking errors converge to the required accuracy through the adaptive control algonthm denved by combmmg the vanable neural network and Lyapunov synthesis techniques.

Observer-Based Discrete-Time Sliding Mode Controller for Benchmark Problem

The discrete-time sliding mode controllers reported in the past had neglected the computational delay that is inherent in any digital implementation. An observer-based discrete-time sliding mode controller was suggested to explicitly account for this delay. The design and analysis of an observer-based discrete-time sliding-mode control system is illustrated using a rotational inverted pendulum. A detailed simulation, that includes computational time delay, sampling process and quantization effects, show that the proposed controller perform well in the presence of modeling errors.

Large-sample analysis of MUSIC and Min-Norm direction estimators in the presence of model errors

We analyze the large-sample mean square error (MSE) of MUSIC and Min-Norm direction-of-arrival (DOA) estimators under fairly general conditions, including mismodelling of the array response and the noise covariance. We separate the contributions to the MSE into a bias part caused by modelling errors and a variance part caused by finite (yet large) sample effects. The bias is simply evaluated by comparing the limiting estimate (corresponding to an infinite number of snapshots) with the true DOAs (which are known to the analyzer). To simplify the variance derivation we assume that the snapshots are complex i.i.d. Gaussian vectors and that the largest eigenvalues of their covariance matrix are distinct, but,otherwise, make none of the assumptions commonly used in previous analyses; in particular we do not constrain the snapshots to satisfy any model equation. The theoretical results obtained are illustrated by means of numerical examples using various modelling errors.

General framework for asymptotic properties of generalized weighted nonlinear least-squares estimators with deterministic and stochastic weighting

This paper studies the asymptotic properties (strong consistency, convergence rate, asymptotic normality) of a generalized weighted nonlinear least-squares estimator under weak noise assumptions. Both deterministic and stochastic weighting are handled and the presence of model errors is considered. For particular models, estimators, and noise assumptions the general framework boils down to known time and frequency-domain estimators.

Robust Control of Robot Manipulators Based on Joint Torque Sensor Information

This article is concerned with robust control of robot manip ulators in the case where joint torque sensors are available. First, we derive a dynamic equation of the manipulator with joint torque sensors that explicitly expresses a nonlinear mul tivariable structure. This dynamic equation makes it possible to construct the control systems of the manipulators with joint torque sensors based on a similar method used in the conven tional case without the sensors. Second. based on this dynamic equation, we propose a robust trajectory control scheme that achieves the specified tracking accuracy in the presence of modeling error, including the modeling error of actuator sys tems. The proposed method fully exploits joint torque sensor information to compensate the uncertainty of link and load parameters. Furthermore, an illustrative simulation result is given to show the effectiveness of the proposed control method.

Adaptive fading Kalman filter with an application

A new adaptive state estimation algorithm, namely adaptive fading Kalman filter (AFKF), is proposed to solve the divergence problem of Kalman filter. A criterion function is constructed to measure the optimality of Kalman filter. The forgetting factor in AFKF is adaptively adjusted by minimizing the defined criterion function using measured outputs. The algorithm remains convergent and tends to be optimal in the presence of model errors. It has been successfully applied to the headbox of a paper-making machine for state estimation.

Large-Sample Analysis of Music and Min-Norm Direction Estimators in the Presence of Model Errors

We analyze the large-sample mean square error (MSE) of MUSIC and Min-Norm direction-of-arrival (DOA) estimators under fairly general conditions, including mismodelling of the array response and the noise covariance. We separate the contributions to the MSE into a bias part caused by modelling errors and a variance part caused by finite (yet large) sample effects. The bias is simply evaluated by comparing the limiting estimate (corresponding to an infinite number of snapshots) with the true DOA’s (which are known to the analyzer). To simplify the variance derivation we assume that the snapshots are complex i.i.d. Gaussian vectors and that the largest eigenvalues of their covariance matrix are distinct; but, otherwise, make none of the assumptions commonly used in previous analyses; in particular we do not constrain the snapshots to satisfy any model equation. The theoretical results obtained are illustrated by means of numerical examples using various modelling errors.

Generalized rank annihilation method. III: Practical implementation

AbstractIn this paper we discuss the practical implementation of the generalized rank annihilation method (GRAM). The practical implementation comes down to developing a computer program where two critical steps can be distinguished: the construction of the factor space and the oblique rotation of the factors. The construction of the factor space is a least‐squares (LS) problem solved by singular value decomposition (SVD), whereas the rotation of the factors is brought about by solving an eigenvalue problem. In the past several formulations for GRAM have been published. The differences essentially come down to solving either a standard eigenvalue problem or a generalized eigenvalue problem. The first objective of this paper is to discuss the numerical stability of the algorithms resulting from these formulations. It is found that the generalized eigenvalue problem is only to be preferred if the construction of the factor space is not performed with maximum precision. This is demonstrated for the case where the dominant factors are calculated by the non‐linear iterative partial least‐squares (NIPALS) algorithm. Several performance measures are proposed to investigate the numerical accuracy of the computed solution. The previously derived bias and variance are proposed to estimate the number of physically significant digits in the computed solution. The second objective of this paper is to discuss the relevance of theoretical considerations for application of GRAM in the presence of model errors.

Effects of modeling errors on the resolution threshold of the MUSIC algorithm

Subspace-based algorithms for narrowband direction-of-arrival (DOA) estimation require detailed knowledge of the array response (the array manifold) and assume that the noise covariance matrix is known up to a scaling factor. In practice, these quantities are not known precisely. Estimation accuracy can degrade significantly when the array response or the noise covariance deviate from their nominal values. In the paper the authors examine the resolution threshold of the MUSIC algorithm when the array response is perturbed from its assumed value and when the noise covariance does not match the assumed model. Analytical expressions for the resolution threshold are derived and verified by computer simulation. The authors also demonstrate the fact that preprocessing of the array data can improve somewhat the resolution in the presence of model errors. The paper makes extensive use of the contributions of various authors.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>